Any finite simple graph $G = (V,E)$ can be represented by a collection $\mathscr{C}$ of subsets $V$ such that $uv\in E$ if and only $u$ $v$ appear together in an odd number sets $\mathscr{C}$. Let $c_2(G)$ denote the minimum cardinality collection. This invariant is equivalent to dimension faithful orthogonal representation $G$ over $\mathbb{F}_2$ closely connected rank $G$. We show $c_2(G) \op...

An active area of research in computational science is the design algorithms for solving subgraph matching problem to find copies a given template graph larger world graph. Prior works have largely addressed single-channel networks using variety approaches. We present suite filtering methods isomorphisms multiplex (with different types edges between nodes and more than one edge within each chan...

this article proposes an optimization model for preventing the waste of time in the educational and research activities' cycle of an organization such as a university. for this purpose and in order to increase efficiency and prevent the waste of time; the graph theory models have been used. the educational and research activities diagrams of a supposed university is drawn by the use of graphs t...

This paper introduces the largest connected subgraph game played on an undirected graph G. In each round, Alice first colours uncoloured vertex of G red, and then, Bob blue, with all vertices initially uncoloured. Once are coloured, (Bob, resp.) wins if there is a red (blue, whose order greater than any blue (red, subgraph. We prove that, plays optimally, then can never win, define large class ...